We extend the Kerr-Schild double copy to the case of a probe particle moving in the Kerr-Schild background. In particular, we solve Wong's equations for a test color charge in a Coulomb non-Abelian potential ($\sqrt{\text{Schw}}$) and on the equatorial plane for the potential generated by a rotating disk of charge known as the single copy of the $\text{Kerr}$ background ($\sqrt{\text{Kerr}}$). The orbits, as the corresponding geodesics on the gravity side, feature elliptic, circular, hyperbolic and plunge behaviour for the charged particle. We then find a new double copy map between the conserved charges on the gauge theory side and the gravity side, which enables us to fully recover geodesic equations for Schwarzschild and Kerr. Interestingly, the map works naturally for both bound and unbound orbits.

Geodesics From Classical Double Copy

Nonlinear (chiral) p-form electrodynamics

We briefly review and critically compare three approaches to constructing Lagrangian theories of self-interacting Abelian chiral form fields with manifest Lorentz invariance. The first approach relies on the original ideas of Pasti, Sorokin, and Tonin (PST) and has been explored since the late 1990s. The second approach was introduced by Ashoke Sen in 2015. The third approach has been developed over the last few years in the works of the present authors and other collaborators and may be called the 'clone field' formalism since it features an auxiliary 'clone' of the gauge field sector. We argue that this last approach shares the attractive features of the other two while avoiding their respective shortcomings. Like in Sen's approach, within the clone field formalism, arbitrary interactions can be straightforwardly included in any number of dimensions (treating interactions becomes very difficult in the PST formalism in dimensions greater than 6). Like in the PST approach, all the auxiliary fields are gauged away on-shell (while in Sen's approach, they merely decouple from the physical fields but remain dynamical). 

Three approaches to chiral form interactions

Motivated by Sen’s spacetime prescription for the construction of theories with self-dual ﬁeld strengths, we present a rigid superspace Lagrangian describing noninteracting tensor multiplets living on a stack of M5-branes and containing all the physical constraints on the ﬁelds, yielding the on-shell matching of the degrees of freedom. The geometric superspace approach adopted here oﬀers a natural realization of superdiﬀeomorphisms and is particularly well suited for the coupling to supergravity. However, within this formulation the (anti-)self-duality property of the 3-form ﬁeld strengths is lost when the superspace Lagrangian is trivially restricted to spacetime. We propose two main paths to address this issue: a ﬁrst-order superspace extension of Sen’s spacetime results, which, once trivially restricted to spacetime, yields all the dynamical equations including the (anti-)self-duality constraint on the 3-form ﬁeld strengths, and a possible way to obtain a full superspace description of the theory, based

M5-brane in the superspace approach

Chiral bosons, or self-dual p-form fields, are ubiquitous in string theoretic contexts but are challenging to treat. Lagrangian constructions invariably introduce a complexity be it auxiliary fields or sacrificing Lorentz invariance. In this note we show how to pass between such different approaches to chiral bosons starting from a Chern Simons point of view to recover formulations of Pasti, Sorokin and Tonin and of Mkrtchyan. This leads to a novel generalisation of the latter to include non-Abelian chiral bosons in 2-dimensions, and generalisations to include twisted self-duality which are relevant in T-duality symmetric approaches to string theory. Our approach also shows how global affine symmetries of two- and higher-dimensional chiral bosons emerge from broken Chern-Simons gauge transformations on the boundary.

Unifying approaches to chiral bosons

We explore the properties of polynomial Lagrangians for chiral p-forms previously proposed by the last named author, and in particular, provide a self-contained treatment of the symmetries and equations of motion that shows a great economy and simplicity of this formalism. We further use analogous techniques to construct polynomial democratic Lagrangians for general p-forms where electric and magnetic potentials appear on equal footing as explicit dynamical variables. Due to our reliance on the differential form notation, the construction is compact and universally valid for forms of all ranks, in any number of dimensions.

/pdf/polynomial-duality-symmetric-lagrangians-for-free-p-forms-2goe6jja3b.pdf

Polynomial duality-symmetric lagrangians for free p-forms

We construct a generalisation of the three-dimensional Poincare algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincare gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincare symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.

/pdf/colourful-poincare-symmetry-gravity-and-particle-actions-4d0f4b4p68.pdf

Colourful Poincaré symmetry, gravity and particle actions

We explore the properties of polynomial Lagrangians for chiral $p$-forms previously proposed by the last named author, and in particular, provide a self-contained treatment of the symmetries and equations of motion that shows a great economy and simplicity of this formalism. We further use analogous techniques to construct polynomial democratic Lagrangians for general $p$-forms where electric and magnetic potentials appear on equal footing as explicit dynamical variables. Due to our reliance on the differential form notation, the construction is compact and universally valid for forms of all ranks, in any number of dimensions.

/pdf/polynomial-duality-symmetric-lagrangians-for-free-p-forms-3k1b01sugh.pdf

Karapet Mkrtchyan

Papers

Polynomial duality-symmetric lagrangians for free p-forms

Colourful Poincaré symmetry, gravity and particle actions

Polynomial Duality-Symmetric Lagrangians for Free p-Forms